The term "love" merely seems to be addressed to the woman, presumably his wife, with whom he is sharing a room with a view of the English Channel and Dover Beach at night. The entire poem is addressed to this woman he loves. She must be someone who knows him well, and someone to whom he feels free to share his innermost thoughts. It might be speculated that they are on their honeymoon. Since he asked her at the start of the poem to come to the window, we can assume that she is standing beside her and gazing out the window with him when he calls her "love" and speaks the most moving lines, suggesting that the whole world is descending into chaos and they have only each other to cling to in the void.
The technique in Matthew Arnold's poem might be compared with that of William Wordsworth's "Lines Written a Few Miles Above Tintern Abbey: On Revisiting the Banks of the Rye During a Tour, July 13, 1798," which are putatively addressed to Wordsworth's sister Dorothy, as revealed in the following:
"For thou art with me, here, upon the banks
Of this fair river; thou, my dearest Friend,
My dear, dear Friend, and in thy voice I catch
The language of my former heart, and read
My former pleasures in the shooting lights
Of thy wild eyes. Oh! yet a little while
May I behold in thee what I was once,
My dear, dear Sister!